An approach to the non-linear mathematical modelling and the numerical simulation of once-through subcritical steam generator dynamics

Abstract

A non-linear lumped-parameter mathematical model of once-through subcritical steam generator dynamics is derived and discussed. This model is decoupled into four section submodels. It uses section outlet conditions as the section representative conditions and assumes that the dynamics of the time-varying phase boundaries is much faster than the dynamics of the metal temperature, fluid temperature, density and internal energy. The derived model is simpler and has better numerical stability and calculation speed characteristics compared with the model given in Reference 1. This paper also proposes a fast and numerically stable algorithm for the numerical simulation of once-through subcritical steam generator dynamics. This algorithm is based, on one hand, on the linearization of the implicit part in the multi-step solution of the set of differential equations and, on the other hand, on the simultaneous solving of the set of differential equations and the set of algebraic equations. The proposed algorithm avoids the problem of numerical instability and enables the use of large time steps and fast computation speed. The algorithm is applied non-iteratively and with triangular factorization of the Jacobian matrix only in the first few time steps. The four section submodels are solved separately by successivel in a uniquely defined order.